Scheduling – Heavy Topspin

November 25, 1973: Play On

Tennis never had an official offseason. The global nature of the sport ensured there was always some place to play: Australia in December and January, the French Riviera or the Caribbean (or indoors!) in February and March, then Europe and North America straight through to September or October. Individual athletes could take time off, and many did. But there was never a true break.

The schedule became even more crowded in the early 1970s as promoters seized the opportunities of the Open era and the ensuing tennis boom. Circuits in the United States hit the gas in January and didn’t ease up until May. New destinations such as Japan to Iran plugged gaps in the fall. If a marquee name somehow ended up with a free date, an exhibition could be arranged anywhere from Hawaii to Whitefish Bay, Wisconsin.

On November 25th, 1973, Arthur Ashe had a day off in Johannesburg ahead of his final against Jimmy Connors. He gave a clinic in the township of Soweto, earning legions of new fans and expanding his horizons still further on his historic trip.

Ashe and Connors, it seemed, were the only stars not in action on this day, eleven months after they kicked off their 1973 campaigns. Elsewhere on the 25th:

Rosie Casals beat Billie Jean King for the title at the Lady Baltimore tournament, a charity benefit for, among other beneficiaries, the Medical Eye Bank of Maryland. Both women showed signs of rust, but Rosie’s intensity was hardly dimmed. Angered by a pair of bad calls in the third set, she loudly asked if the linesman had recently donated to the eye bank.
In Buenos Aires, home favorite Guillermo Vilas outlasted Björn Borg for the title at the Argentine Open. The duel had the makings of a classic as it headed to a fourth-set tiebreak with Vilas leading two sets to one. But Borg injured his hand and called it a day. It was the first meeting between the pair, who would face off more than 20 times before the end of the decade, including twice for the French Open title.
Remarkably, that wasn’t the only victory Vilas tallied that day without winning a match point. He and countryman Ricardo Cano had split sets with Ion Țiriac and Jean-Baptiste Chanfreau, the score standing 4-6, 7-5, 3-2 in favor of the latter, when the umpire changed a call that had initially gone against the Argentinians. Țiriac stormed off, handing the semi-final to Vilas and Cano by default.
Jiří Hřebec proved that his Davis Cup heroics were no fluke by winning the South Australian Championships in Adelaide. It was his second title in a month–and his second ever. The 23-year-old Czechoslovakian continued to get help from his teammates: His opponent in the final, Bob Giltinan, was exhausted after a five-setter the previous day against Jan Kodeš. Hřebec won in four.
Even with the 1973 Davis Cup still in play, the 1974 competition was gaining steam. On the 25th, Mexico wrapped up a preliminary-round defeat of Canada, while Colombia edged out Venezuela. Canada was already contesting its second tie for the ’74 Cup; they had beaten the Caribbean/West Indies team in October. Mexico and Colombia would play in December, with the winner advancing to challenge the United States in January.
At the Port Washington Tennis Academy in New York–the training facility run by legendary Australian coach Harry Hopman–several national indoor champions were minted in the 14-and-under and 12-and-under categories. The match of the day decided the 12s title, which Californian Kelly Henry lost in three sets to an astonishing ten-year-old backboard named Tracy Austin.

The stars who weren’t in Johannesburg (or Adelaide, or Baltimore, or Buenos Aires, or Mexico City) were practicing hard. The Davis Cup final was only a few days away, with the Grand Prix Masters to follow. After that, maybe a week or two at home, and the whole cycle would begin again.

* * *

This post is part of my series about the 1973 season, Battles, Boycotts, and Breakouts. Keep up with the project by checking the TennisAbstract.com front page, which shows an up-to-date Table of Contents after I post each installment.

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Podcast Episode 97: Matt Futterman on the Australian Open and Sports With Fans

This week’s guest is Matt Futterman, reporter for the New York Times and author of Running to the Edge: A Band of Misfits and the Guru Who Unlocked the Secrets of Speed and Players: How Sports Became a Business.

Matt, who spent 15 days in hotel quarantine so that he could cover the Australian Open, talks about his time in isolation and what is was like to emerge into a semblance of normal life. He explains why sports aren’t really sports without fans, how close the Australian Open came to not happening, and why Sofia Kenin isn’t a bigger star.

I also take advantage of Matt’s extensive knowledge of distance running to ask whether the unique schedules of marathoners provide any insight into how tennis players can better manage the pandemic, how tennis pros can gain some of the benefits of being part of a team, and which active player would run the fastest marathon.

Thanks for listening!

(Note: this week’s episode is about 48 minutes long; in some browsers the audio player may display a different length. Sorry about that!)

Click to listen, subscribe on iTunes, or use our feed to get updates on your favorite podcast software.

Podcast housekeeping:

In case you haven’t heard, I’m one month into a short (~4 minutes) daily podcast called Expected Points. Here’s today’s episode.
The TAP book club will reconvene next week with our next selection, John Updike’s 1968 novel, Couples. Read along with us, share your thoughts, and suggest topics/questions/comments for our discussion in a future episode. (Yes, I know I said “next week” last week, too. This time I mean it. Probably.)

The Best Draw That Money Can Buy

Italian translation at settesei.it

Last week featured two events on the WTA calendar. First, both chronologically and by every conceivable ranking except for “most Hungarian,” was the Dubai Open, a Premier 5 event offering over $500,000 and 900 ranking points for the winner. The other was the Hungarian Open in Budapest, a WTA International tournament with $43,000 and 280 ranking points going to the champion. No top player would seriously consider going to Budapest, even before considering potential appearance fees and WTA incentives.

Fifteen of the top twenty ranked women went to Dubai, and the top seed in Budapest, defending champ Alison Van Uytvanck, was ranked 50th. Every Budapest entrant ranked in the top 72 got a top-eight seed, including a couple of players who would have needed to play qualifying just to earn a place in the Dubai main draw.

The rewards offered by the Dubai event and supported by the structure of the WTA tour make this an easy scheduling decision for many players. But at some point, if the rest of the field is zigging toward the Gulf, might it be better to zag toward Central Europe? Van Uytvanck would have been an underdog to reach even the third round of the richer event, yet she defended her title in Budapest. Marketa Vondrousova, who would have been stuck in Dubai qualifying, reached the Hungarian Open final. Opting for the smaller stage almost definitely proved the wise choice for those two women. Did other, better-ranked players leave money or ranking points on the table?

Motivations

Scheduling decisions depend on a lot of factors. Some women might prefer to play the event with the highest-quality field, both to test themselves against the best and to give themselves an opportunity for the circuit’s richest prizes. Others might head for the marquee events because of their doubles prowess: Timea Babos was part of the top-seeded doubles team in Dubai, but was the lowest-ranked direct entry in singles. Still others might choose to play closer to home or at tournaments they’ve enjoyed in the past.

For all that, ranking points should come first, with prize money also among the top considerations. Ranking points determine one’s ability to enter future events and to remain on tour. Prize money is necessary to cover the vast expenses necessary to bankroll a traveling support staff.

Dubai-versus-Budapest offers a fairly “pure” experiment, because both are played on similar surfaces and neither event is in the middle of a mini-circuit of events in a single region. Yes, Dubai immediately follows Doha, but that trip requires a flight, and most players headed back to Europe or North America after the tournament. Opting for one event over the other doesn’t substantially complicate anyone’s travel plans, like it would for an ATPer to mix and match destinations from the South American golden swing and the simultaneous European indoor circuit.

Revealed preferences

Let’s see which of the two main factors played a bigger role in scheduling decisions last week. To determine each player’s options, I tried to reconstruct as much as possible what information each woman had at her disposal six weeks earlier, on January 7th, when entry applications and stated preferences for Dubai and Budapest were due. I used the January 7th rankings to project how a player would be seeded at either event, and Elo ratings as of that date to forecast how far she would advance in each draw.

The major difficulty of this kind of simulation is the composition of the draws themselves. From our vantage point after the events, we know who opted for each draw as well as which players were unable to compete. In early January, none but the best-connected players would have known which of her peers would head in which direction, and no one at all could have known that Caroline Wozniacki would be a late withdrawal from Dubai, or that a viral illness would knock Kirsten Flipkens out of the Hungarian Open. Still, the resulting 2019 draws were very similar to what players could have predicted based on the player fields in 2018. So to simulate each player’s options, we’ll use the fields as they turned out to be.

Let’s start with Carla Suarez Navarro, the highest-ranked woman (at the January 7th entry deadline) who wasn’t seeded in Dubai. She ended up reaching the quarter-finals at the Premier event, in part because Kristina Mladenovic did her the favor of ousting Naomi Osaka from that section of the draw. For her efforts, Suarez Navarro grabbed 190 ranking points and almost $60,000. She would have needed to win the Budapest title to garner more points. And with a champion’s purse of “only” $43,000 in Hungary, she would have needed to rob a bank to improve on her Dubai prize money check.

However, that isn’t what Suarez Navarro should have anticipated taking home from Dubai. Sure, she should be optimstic about her own potential, but smart scheduling demands some degree of realism. I ran simulations of both the Dubai tournament (before the draw was made, so she doesn’t always end up in Osaka’s quarter) and the Budapest event with the Spaniard as the top seed and the rest of the field (minus last-in Arantxa Rus) unchanged. These forecasts suggest that Suarez Navarro only had a 12% chance of reaching the Dubai quarters, and that her expected ranking points in the Gulf were much lower:

Event     Points  Prize Money  
Dubai         76     $28.121   
Budapest     111     $15.384

(prize money in thousands of USD)

In all of these simulations, I’ve calculated points and prize money as weighted averages. Suarez Navarro had a 37% chance of a first-round loss, so that’s a 37% chance of one ranking point and first-round-loser prize money. And so on, for all of the possible outcomes at each event. For the Spaniard, her expected ranking points were nearly 50% higher as the top seed in Budapest. But because the Dubai prize pot is so much larger, her expected check was almost twice as big at the tournament she chose.

Consistent incentives

The total purse in Dubai was more than eleven times bigger than the prize money on offer in Hungary, while the points differed by only a factor of three. Thus, it’s no surprise that Suarez Navarro’s incentives are representative of those faced by many more women. I ran the same simulations for 26 more players: All of the competitors who gained direct entry into Dubai but were unseeded, plus Bernarda Pera, who would have been seeded in Budapest but instead played qualifying in the Gulf.

The following table shows each player’s expected points and prize money for Dubai (D-Pts and D-Prize), along with the corresponding figures for Budapest (B-Pts and B-Prize):

Player                    D-Pts   D-Prize   B-Pts   B-Prize   
Dominika Cibulkova           96   $36.794     130   $18.291   
Lesia Tsurenko               84   $31.528     119   $16.695   
Carla Suarez Navarro         76   $28.121     111   $15.384   
Aliaksandra Sasnovich        75   $27.920     111   $15.364   
Dayana Yastremska            72   $26.716     107   $14.803   
Anastasia Pavlyuchenkova     72   $26.590     106   $14.721   
Barbora Strycova             67   $24.809     102   $14.096   
Donna Vekic                  66   $24.143     100   $13.717   
Katerina Siniakova           63   $23.157      95   $13.062   
Ekaterina Makarova           58   $21.543      90   $12.265   
                                                              
Player                    D-Pts   D-Prize   B-Pts   B-Prize   
Petra Martic                 57   $21.019      88   $11.960   
Su Wei Hsieh                 54   $19.863      84   $11.396   
Belinda Bencic               53   $19.813      84   $11.372   
Ajla Tomljanovic             53   $19.530      82   $11.181   
Shuai Zhang                  49   $18.350      77   $10.416   
Sofia Kenin                  46   $17.109      72    $9.659   
Ons Jabeur                   45   $17.077      71    $9.624   
Viktoria Kuzmova             45   $17.009      70    $9.432   
Alize Cornet                 44   $16.823      69    $9.280   
Saisai Zheng                 40   $15.436      62    $8.307   
                                                              
Player                    D-Pts   D-Prize   B-Pts   B-Prize   
Vera Lapko                   37   $14.618      57    $7.695   
Mihaela Buzarnescu           36   $14.465      56    $7.548   
Alison Riske                 35   $14.309      55    $7.445   
Kristina Mladenovic          34   $13.910      51    $6.969   
Timea Babos                  32   $13.354      48    $6.572   
Yulia Putintseva             32   $13.407      48    $6.484   
Bernarda Pera*               25   $11.830      36    $5.061

Every single player could have expected more points in Budapest and more money in Dubai. The ratios are all similar to Suarez Navarro’s. The one possible expection is Pera (hence the asterisk). My simulation assumed she came through qualifying to make the main draw, and calculated only her expected points and prize money from main draw matches. Yet simply qualifying for the main draw is worth 30 ranking points, plus whatever points a player earns by winning main draw matches. Pera was no lock to qualify, but she was favored, and usually a couple of lucky loser spots make the main draw even more achieveable. It’s possible that if we ran all those scenarios, Pera is the one player for whom Dubai offered better hopes of prize money and points.

Loss aversion and game theory

It’s no accident that Van Uytvanck was one of the few players to choose the high-points, low-prize money route. She was defending 280 points from last year’s Hungarian Open, meaning that opting for a bigger check in Dubai would have a negative impact on her ranking. The thought of losing a couple hundred ranking points has a greater influence on behavior than the chance of gaining the same amount for a player who has few to defend.

For the majority of women who will face the same decision in 2020 without many points to defend, what should they do? Assuming, as I do, that they and their coaches will all carefully study this article, what happens if more top-70 players decide to chase ranking points and flock to the smaller event?

If the Budapest field gets stronger, each entrant’s expected points and prize money will decrease; if Dubai’s field weakens, each player there can anticipate a better chance of more points and even more money. As the entry system is currently structured, in which each player must state their preferences without knowledge of their peers’ choices, we can’t count on reaching an equilibrium. Even if every single player aimed solely to maximize ranking points, there wouldn’t be enough information available to reliably make the right choice. It’s conceivable, though unlikely, that a Budapest could attract a stronger field and end up offering lower expected prize money checks and ranking points.

But don’t fret, dear readers and schedule optimizers. There are external factors and there always will be. And in this case, virtually all of those factors pull players to the bigger money event. (Even Hungarian heroine Babos skipped her home tournament.) At least a half-dozen of the players listed above are doubles elites, making it likely they’ll choose the Premier event. Others–probably many others–will go where the money is, because they like money.

Even those who don’t play doubles and don’t like money will chase the biggest available pot of ranking points, not entirely unlike the way people play the lottery. The WTA offers a very limited set of opportunities to earn 900 points in a single week. You can get close to 900 points with three International championships, but there’s a finite number of weeks on the annual schedule–not to mention a limited number of matches in each player’s body! Lots of people stock up on lottery tickets despite unfavorable odds, and players will continue to enter higher-profile events even if their expected points are higher on smaller stages. The chance of a prestigious title, however slim, doesn’t show up in a purely actuarial calculation.

The success of Belinda Bencic–expected Dubai points, 53; expected Budapest points, 84; actual Dubai points, 900–will keep players chasing the big prizes. That’s good news for level-headed would-be optimizers. Those players willing to forego the skyscrapers, the shopping malls, and the prize money next year aren’t about to lose this opportunity. Budapest will almost certainly remain a better option for players who want to improve their ranking.

The Proud Tradition of Americans Skipping Monte Carlo

Italian translation at settesei.it

The Monte Carlo Masters is unique among the ATP’s 1,000 series events. The stakes are high, but attendance isn’t mandatory, so while most of the game’s top players show up, a few take the week off. No group has so consistently skipped Monte Carlo than players from the U.S.A.

This year, six U.S. players had rankings that would’ve gotten them into the Monte Carlo main draw, where winning a single match earns you 45 ranking points and just over €28,000 in prize money. Five of those players–including John Isner, who reached the third round two years ago and won a pair of tough Davis Cup matches at the same venue–opted out. All five played the 250-level Houston tournament last week instead. Only Ryan Harrison made the trip to Europe–losing in the opening round, as Carl Bialik and I safely predicted on this week’s podcast.

Choosing the low-stakes event on home soil isn’t the wise choice, but it’s nothing new. Since 2006, only seven Americans have appeared in a Monte Carlo main draw: Isner twice, Harrison, Sam Querrey, Donald Young, Steve Johnson, and Denis Kudla, who qualified in 2015. From 2006 to 2016, 7 of the 11 Monte Carlo draws were entirely USA-free. In the same time span, Houston draws have featured 35 Americans ranked in the top 60–all players who probably would have earned direct entry in the higher-stakes clay event, as well.

For a player like Isner or Jack Sock, an April schedule can handle both tournaments. Four of the seven Americans who went to Monte Carlo played Houston as well, including Querrey in 2008, when he lost in the first round in Houston but reached the final eight in Monte Carlo.

Most U.S. players, including just about everyone I’ve mentioned so far, would much rather play on hard courts than on clay. (The Houston surface is more conducive to aggressive, first-strike tennis than is the Monte Carlo dirt, one of the slowest surfaces on the calendar.) However, as Isner and Querrey have shown, a one-dimensional power game can succeed on a slow court, even if it looks nothing like the strategy of a traditional clay specialist.

Isner, in particular, has racked up plenty of points on the surface. While he’d much rather play on home soil, he has twice reached the fourth round at the French Open and pushed none other Rafael Nadal to a deciding set in both Paris and Monte Carlo. Sock is also a threat on the surface, having won nearly two-thirds of his tour-level matches on clay. Many of those wins came in Houston, but like Isner, he took a set from Nadal in Europe on the surface the Spaniard typically dominates.

Even if the top Americans had little chance of going deep in Monte Carlo, one wonders what the additional time on the surface would do for the rest of their clay season. Most will show up for Madrid and Rome, and all of them will play Roland Garros. It’s a bit of a chicken-and-egg question–do Americans avoid the dirt because they suck on clay, or do they suck because they avoid it?–but it couldn’t hurt to play on the more traditional European surface against elite-level opponents.

The difference in rewards between a 250 like Houston and a Masters 1000 like Monte Carlo make it likely that the risk of playing in unfamiliar territory would pay off, as it did for Querrey in his one trip and for Isner two years ago. And I suspect that the rewards would stretch beyond the immediate shot at a bigger payday: If someone like Sock invested more time in developing his clay-court game now, he could become a legitimate threat at a faster clay tournament (such as the Madrid Masters) in a few years. It’s probably too late for the likes of Querrey, but the next generation of U.S. men’s stars would do well to break with tradition and give themselves more chances to excel on the dirt.

Cool Down Tennis

This is a guest post by Carl Bialik.

Imagine you’re named boss of tennis. Right after being sworn in by Rod Laver and Martina Navratilova, you’re handed an empty wall calendar. You make the schedule for 2018. What’s your first move?

Mine would be to move Indian Wells and Miami earlier in the calendar, and the Australian Open later, after the two U.S. Masters tournaments.

I never wanted this more than while sweating my way around the Indian Wells grounds in search of shade last month. I wasn’t alone. The only full sections of the main stadium during day sessions were the ones protected from the sun. Around the fan-friendly venue, there are plenty of seats in the shade — under tents, or in Adirondack chairs that shade-seeking people push ever closer to the screen as the sun shifts. The players can only wait for shade to slowly descend on the court. Jack Sock needed a towel holding 50 ice cubes to cool down.

Sure, it was unusually hot at this year’s Indian Wells tournament. But the climatological averages are clear: It’s hot in the California desert and in the Florida sunshine in March, and in the antipodean summer in January. It’d be cooler in Indian Wells, Miami and Melbourne if the two Masters events moved two months earlier and led up to the year’s first Grand Slam in March. Each of the two-week events would be, on average, 4 to 10 degrees Fahrenheit cooler each year. (The precipitation would be about the same, so Miami men’s finalist Rafael Nadal might continue to bemoan humidity, request sawdust and show more than he’d planned beneath his shorts; while women’s champ Johanna Konta might keep having to change clothes midmatch because they’ve accumulated approximately five kilograms of sweat.)

I’m using the averages because I don’t want to make too much of an unseasonably hot Indian Wells, or too little of an unusually cold March in Miami. But the averages might understate the problem because it’s precisely the outliers we’re worried about. A nudge downward of a few degrees, on average, could translate into a big drop in the probability of an unbearably hot fortnight — say, from 25 percent to 5 percent.

Changing the tennis calendar would also mean less daylight. That wouldn’t be so good for the nickname Sunshine Double, but it’d be good for tennis. Until more tennis stadiums adopt overhanging partial roofs — but for sun, not for rain — shorter days means less sun for fans to contend with and more reason to fill the seats. Plus, night tennis is exciting. The venues already have plenty of lights and evening sessions.

Scrambling the schedule would do more than cool down tennis. The three midyear majors’ proximity to each other helps the sport carry some momentum and mainstream buzz from one to the next. The Australian Open squanders all that in the four-month gap between its end and the start of the French Open. There’s even a month between the Aussie Open and the next big event.

The other three majors also get opening acts, to help players build up familiarity with the surface and for fans to build anticipation. The Australian Open gets two weeks at the start of the season — without so much as a 500 event on the men’s side.

The lack of buffer between the offseason and Melbourne also means it loses some players still recovering from the end of the previous season. That was the case this year with Juan Martin del Potro, who skipped this year’s first major after winning the Davis Cup with Argentina in November.

Imagine instead starting the season with Indian Wells and Miami — or Miami, then Indian Wells, while we’re scrambling things, for the convenience of travel from the sport’s power center of Europe — using the same courts and balls as Melbourne. Follow that month — or less, if one or both of the U.S. early-year Masters succumbs to the reality that they could be just a week — by Doha and Dubai, then Brisbane, Sydney and the like, before the main event in Melbourne at the start of March. We’d start the season with a real hard-court swing, ending with the first major.

From Australia, the tour could stay in the southern hemisphere. The swing through South America has a long history and a terrible spot on the current calendar. It was traditionally played on clay but some of its biggest events are moving to hard courts — first (North American) Acapulco, now, maybe, Rio, in search of Masters status — to the chagrin of Nadal and others. Too many players simply don’t think it’s worth it to compete on clay for a few weeks if that’s followed by a month of hard-court events. But move Indian Wells and Miami, and South American clay could move a month later in the calendar — while slightly tempering what Nadal bemoans as “too extreme” weather conditions by an average of 1 degree. The swing would give way seamlessly to Houston, Charleston and the European clay spell — which, by the way, would absorb Bucharest, Hamburg, Umag, Bastad and Gstaad from their awkward post-Wimbledon calendar slots. And no one would suggest Miami move to green clay.

We’d be left with a coherent calendar with five seasons of roughly equal length and importance, four with a major and one with the year-end finals: (1) Outdoor hard courts in the U.S., the Middle East and Oceania, followed by (2) clay in the Americas and Europe, (3) English and German grass (with Newport for those who want to visit the sport’s hall of fame), (4) North American and Asian outdoor hard courts, and (5) European indoor hard courts (absorbing the current winter events such as St. Petersburg and Rotterdam) culminating in wherever the tours’ multiplying year-end finals are calling home that year. And let’s play Davis Cup and Fed Cup at the same time — the tours acting in sync; what a concept! — on weekends at the edge of the five new seasons, giving hosts a wider range of sensible surfaces to choose from, and creating the option for combined venues if men and women from the same country are hosting the same round. (Prague in 2012 would’ve been tennis nirvana.) Or, hell, consider merging the events.

Could all this happen? Sure — if tennis power were centralized in a person or people who prioritize the overall good of the global game. Without a radical transformation of tennis, though, it’ll be slow going: It took years for the idea of lengthening the grass-court season by a week to become reality.

Carl Bialik has written about tennis for fivethirtyeight.com and The Wall Street Journal. He lives and plays tennis in New York City and has a Tennis Abstract page.

Is Grand Slam Qualifying Worth Tanking For?

Italian translation at settesei.it

Earlier today in Hobart, Naomi Osaka lost her second-round match to Mona Barthel. Coming into the match, she was in a tricky position: If she won, she wouldn’t be able to play Australian Open qualifying. For a young player outside the top 100, a tour-level quarterfinal would be nice, but presumably Melbourne was intended to be the centerpiece of her trip to Australia.

Since she lost the match, she’ll be able to play qualifying. But what if she hadn’t? Is this a situation in which a player would benefit from losing a match?

Put another way: In a position like Osaka’s, what are the incentives? If she could choose between the International-level quarterfinal and the Slam qualifying berth, which should she pick? Or, put more crassly, should a player in this position tank?

Let’s review the scenarios. In scenario A, Osaka wins the Hobart second-rounder, reaches the quarterfinal, and has a chance to go even further. She can’t play the Australian Open in any form. In scenario B, she loses the second-rounder, enters Melbourne qualifying and has a chance to reach the main draw.

Before we go through the numbers, take a guess: Which scenario is likely to give Osaka more ranking points? What about prize money?

Scenario A is more straightforward. By reaching the quarterfinals, she earns 30 additional ranking points and US$2,590 beyond what a second-round loser makes. Beyond that, we need to calculate “expected” points and prize money, using the amounts on offer for each round and combining them with her odds of getting there.

Let’s estimate that Osaka would have about a 25% chance of winning her quarterfinal match and earning an additional 50 points and $5400. In expected terms, that’s 12.5 points and $1,350. If she progresses, we’ll give her a 25% chance of reaching the final, then in the final, a 15% chance of winning the title.

Adding up these various possibilities, from her guaranteed QF points to her 0.94% chance (25%*25%*15*) of winning the Hobart title, we see that her expected rewards in scenario A are roughly 48 ranking points and just under $4,800.

Scenario B starts in a very different place. Thanks to the recent increases in Grand Slam prize money, every player in the qualifying takes home at least US$3,150. That’s already close to Osaka’s expected financial reward from advancing in Hobart. The points are a different story, though: First-round qualifying losers only get 2 WTA ranking points.

I’ll spare you all the calculations for scenario B, but I’ve assumed that Osaka would have a 70% chance of winning qualifying round 1, a 60% chance of winning QR2, and a 50% chance of winning QR3 and qualifying. Those might be a little bit high, but if they are, consider it compensation for the possibility that she’ll reach the main draw as a lucky loser. (Also, if we knock her chances all the way down to 50%, 45%, and 40%, the conclusions are the same, even if the points and prize money in scenario B are quite a bit lower.)

Those estimated probabilities translate into an expectation of about 23 ranking points and US$11,100. Osaka isn’t guaranteed any money beyond the initial $3,150, but the rewards for qualifying are enormous, especially compared to the prize money in Hobart. A first-round main draw loser in Melbourne takes home more money than the losing finalist does in Hobart.

And, of course, if she does qualify, there’s a chance she’ll go further. Since 2000, female Slam qualifiers have reached the second round 41% of the time, the third round 9% of the time, the fourth round 1.8% of the time, and the quarterfinals 0.3% of the time. Those odds, combined with her 21% chance of reaching the main draw in the first place, translate into an additional 7 expected ranking points and $2,600 in prize money.

All told, scenario B gives us 30 expected ranking points and US$13,600 in expected prize money.

The Slam option results in far more cash, while the International route is worth more ranking points. In the long term, those ranking points would have some financial value, possible earning Osaka entry into a few higher-level events than she would otherwise qualify for. But that value probably doesn’t overcome the nearly $9,000 gap in immediate prize money.

I hope that no player ever tanks a match at a tour-level event so they can make it in time for Slam qualifying. But if one does, we’ll at least understand the logic behind it.

Should Andy Murray Skip the Tour Finals to Prepare for Davis Cup?

After advancing to the Davis Cup final, Andy Murray floated the idea that he might skip the World Tour Finals to prepare. The Belgian hosts are likely to choose clay for November’s Davis Cup tie (in part to make Murray less comfortable), and if Murray reached the final round in London the week before, he would have only four days off to recover and adjust to the different surface.

A lot of factors will go into Murray’s ultimate decision: how much importance he gives each event, how much he thinks fatigue will affect him, and how likely it is that the ATP would sanction him for skipping a required event. For today, I’ll have to ignore all of those and focus on the one most amenable to analysis: The effect of switching surfaces right before a Davis Cup tie.

Shifting from one surface to another immediately before Davis Cup is common. From 2009 to the present, there have been just over 2,000 World Group, Group 1, and Group 2 Davis Cup singles rubbers, and almost 450 of those involved at least one player who had played the previous week [1] on a different surface. It’s very rare that both players switched surfaces, so we have a sample of 432 matches in which one player changed surfaces from the previous week, and the other player either played or (presumably) prepared on the same surface.

At the simplest level of analysis, the switchers have been surprisingly effective. In those 432 matches between switchers and non-switchers, the switchers won 275, or 63.6% of the time. When we narrow the sample to the 130 times the switcher reached at least the round of 16 the week before Davis Cup (and, thus, had even less time to adjust), the results are surprisingly similar: 82 wins, or 63.1% in favor of the switchers.

Of course, there are all sorts of biases that could be working in favor of the switchers. The better the player, the less likely he can change his schedule to better prepare for Davis Cup, leaving him stuck on the “wrong” surface the week before a tie. And the better the player, the more likely he was a switcher in the smaller sample, one of those who reached the round of 16 the week before.

To evaluate the effect of switching, then, we must proceed with more subtlety. If switchers are more likely to be the favorites, we need to consider each player’s skill level and estimate how often switchers should have won. To do that, we can use JRank, my player rating system with surface-specific estimates for each competitor.

Immediately, we lose about 15% of our sample due to matches involving at least one player who didn’t have a rating at the time [2]. These are almost all Group 2 matches, so its doubtful that we lose very much. In the slightly smaller pool of 361 matches, the switcher won 62.0%, and when the switcher reached the round of 16 the previous week, he won 60.0%.

JRank confirms that the sample is strongly biased toward switchers. The player changing surfaces was favored in 69.8% of these contests. To take an extreme example, Murray went from hard courts at the 2013 US Open to clay courts in the World Group playoff against Croatia. Against Borna Coric, who hadn’t played the week before, Murray was a 99.1% favorite, and of course he won the match.

Once we calculate the probability that the switcher won each of the 361 matches, it turns out that the switchers “should have” won 227, or 62.8% of the time. That’s almost indistinguishable from the historical record, when the switchers won 224 matches. In the smaller sample of 120 matches when the switcher reached the round of 16 the previous week, switchers “should have” won 72 matches. As it happened, they won exactly 72.

In other words, it doesn’t appear to be a disadvantage to play Davis Cup matches on an unfamiliar surface. JRank-based predictions are primarily based on “regular” matches, so if switchers are performing at the level that JRank forecasts for them, they’re playing as well as they would at, say, the third round of a Slam, when the surface is familiar.

This isn’t a clear answer to Murray’s dilemma, of course. If he plays, say, Roger Federer and Novak Djokovic in back-to-back three-setters on Saturday and Sunday, then travels to a different venue, handles tons of press, and practices with a different set of coaches and fellow players before a big match the following Friday, he faces more of a challenge than your typical surface-switcher in our dataset.

However, there’s little evidence that surface-switching alone is a good reason to skip the Tour Finals. If history is any guide, Murray will play very well on the Belgian clay–just as well as he would at the same venue in the middle of the clay season.

Continue reading Should Andy Murray Skip the Tour Finals to Prepare for Davis Cup?